Do one of the following, as appropriate:
(a) Find the critical value $z _ { \alpha / 2 }$
(b) find the critical value $t _ { \alpha / 2 }$
99% ; n=17 ;$\alpha$

is unknown; population appears to be normally distributed.
A) $z _ { \sigma / 2 } = 2.583$
B) $z _ { \sigma / 2 } = 2.567$
C) $t _ { \sigma / 2 } = 2.921$
D) $t _ { \sigma / 2 } = 2.898$

Question

Do one of the following, as appropriate: 
(a) Find the critical value $z _ { \alpha / 2 }$
(b) find the critical value $t _ { \alpha / 2 }$
99% ; n=17 ;$\alpha$

is unknown; population appears to be normally distributed.
A) $z _ { \sigma / 2 } = 2.583$
B) $z _ { \sigma / 2 } = 2.567$
C) $t _ { \sigma / 2 } = 2.921$
D) $t _ { \sigma / 2 } = 2.898$

Quizplus · Accepted Answer

Since the sample size is small (n=17) and the population standard deviation ($\sigma$) is unknown, we use the t-distribution to find the critical value. For a 99% confidence level and n=17, the degrees of freedom (df) is 16 (n-1). The critical value $t _ { \alpha / 2 }$ for df=16 at the 99% confidence level is approximately 2.921.

Do One of the Following, as Appropriate: (A) Find zα/2z _ { \alpha / 2 }zα/2​

Do One of the Following, as Appropriate:
(A) Find $z _ { \alpha / 2 }$